So after the change, when does the execution happens?

df["col2"] = df["col1"].apply(remote_function)

or

df.to_gbq()

if at the later stage, if the user calls exec APIs (such as repr) multiple times, will the function be executed multiple times?

Is there a way that we can add test to ensure that with multiple operations, there won't be redundant function calls?

So after the change, when does the execution happens?

df["col2"] = df["col1"].apply(remote_function)

or

df.to_gbq()

if at the later stage, if the user calls exec APIs (such as repr) multiple times, will the function be executed multiple times?

It would be the latter. After this change the behavior would be same as the standard bigframes behavior - if the result is cached it won't be executed, else it would be.

Is there a way that we can add test to ensure that with multiple operations, there won't be redundant function calls?

It's tied to caching. Chatted with @TrevorBergeron that caching is not a guarantee at this point but more like an internal optimization. Asserting how many times a function was called is a bit of a stretch, just like asserting how many number of sql jobs were run in an operation, so I'd skip adding a test. Let me know if you have s strong opinion otherwise.